A piece of wire 10 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. Find the maximum and minimum possible area that can be enclosed by the wire.

Given :

A piece of wire 10 m long is cut into two pieces.

To Find :

One piece is bent into a square and the other is bent into an equilateral triangle.

Solution :

So, perimeter of triangle is 5 m :

Area of triangle of side a :

Now. we know maximum area of a given perimeter is for equilateral triangle.

3s = 5

Hence, this is the required solution.

the formula of a slope:

we have the points (-2, 7) and (2, 3). substitute: